We derive a model to describe decoherence of atomic clouds in atom-chip traps taking the excited states of the trapping potential into account. We use this model to investigate decoherence for a single trapping well and for a pair of trapping wells that form the two arms of an atom interferometer. Including the discrete spectrum of the trapping potential gives rise to a decoherence mechanism with a decoherence rate $\ensuremath{\Gamma}$ that scales like $\ensuremath{\Gamma}\ensuremath{\sim}{1/r}_{0}^{4}$ with the distance ${r}_{0}$ from the trap minimum to the wire.
We derive a model to describe decoherence of atomic clouds in atom-chip traps taking the excited states of the trapping potential into account. We use this model to investigate decoherence for a single trapping well and for a pair of trapping wells that form the two arms of an atom interferometer. Including the discrete spectrum of the trapping potential gives rise to a decoherence mechanism with a decoherence rate \ensuremathΓ that scales like \ensuremathΓ\ensuremath∼1/r04 with the distance r0 from the trap minimum to the wire.
Since the achievement of Bose-Einstein condensation (BEC), the progress in matterwave \nphysics has been immense. Among the many recent achievements there is \nthe miniaturization of atom traps, demonstration of the superfluid-Mott insulator \nquantum-phase transition in optical lattices and the experimental demonstration of \nthe BEC-BCS crossover in ultra-cold gases. \nMiniaturization of atom traps using micro-structured wires on a chip is one important \nstep towards an on-chip cold-atom device. These so-called \\atom chips" provide \nhigh control and versatility for trapping and guiding the ultra-cold atomic clouds. \nParticularly interesting is the use of these microchips to build mesoscopic devices \nfor cold atomic clouds as, for instance, in the case of an atom-cloud interferometer. \nHowever, these mesoscopic devices require coherent transport of the atom cloud. A \ngeneral method to treat decoherence due to current fluctuations in multi-wire atomchip \ntraps is presented in the rst part of this thesis. The decoherence rate Γ shows a \nstrong dependence on the distance between the wire and the atom cloud, r0, scaling \nas Γ ~ r-4 0 for a single atom waveguide. Considering an interferometer device, a \nstrong dependence of the decoherence rate on the trap geometry is found. \n \nStudying many-body eects in ultra-cold quantum gases is another important \nresearch eld. Experiments using ultra-cold quantum gases in optical lattices have \ndemonstrated the superuid-Mott insulator quantum phase transition and manybody \nentanglement. Optical lattices are based on a periodic modulation of the light \nintensity, generated by retro-reected laser beams. Correlations of the atomic cloud \nbetween dierent lattice sites of the optical lattice play a central role in these manybody \nexperiments. The dierent phases of the superuid-Mott insulator system can \nbe characterized by the dierent behavior of the inter-lattice site correlations. There \nare several numerical methods such as Quantum Monte Carlo (QMC) simulations, \nDensity Matrix Renormalization Group (DMRG) simulations, exact-diagonalization, \nor the Gutzwiller ansatz, to investigate the dynamics of an ultra-cold gas in an optical \nlattice theoretically. The Gutzwiller method, corresponding to the mean-eld solution, \nallows for the treatment of large lattice sizes. Mean-eld approaches have proven \nto be very useful to describe many-body physics. However, diculties arise in the correct \ndescription of the behavior of the decay of inter-lattice site correlations. Based on \nthe Gutzwiller approach, we have developed a method which allows the successive inclusion \nof inter-lattice site correlations. Comparing the results for the particle-number \nuctuations and the correlation function obtained from pure Gutzwiller calculations, \nto calculations which perturbatively include short-range correlations and calculations \n \nusing \\quasi-exact methods", showed a considerable improvement relative to the pure \nGutzwiller results due to the inclusion of short-range correlations. \nMany-body eects do not only arise in periodic potentials, but become increasingly \nimportant at ultra-low temperatures. The formation of Bose-Einstein condensates \nrequires an overlap of the atom wavefunctions and, hence, the formation of \na single condensate wavefunction. Another example of a many-body state is the \nsuperuid-BCS state, commonly used as a description of superconductivity. Here, \nfermions in dierent hyperne states form Cooper pairs. Experiments with ultracold \nquantum gases enable a variation of the interparticle interaction, e.g. , by using \na Feshbach resonance. Using Feshbach resonances to tune the interaction strength \nhas enabled the experimental observation of the crossover from a superuid-BCS \nstate to a Bose-Einstein condensate of molecules. A useful way to characterize the \ndierent states of ultra-cold quantum gases is to investigate the particle-number uctuations. \nIn this thesis we suggest to divide the atomic cloud into bins and consider \nthe atom-number uctuations in these bins. We calculate the full counting statistics \nfor dierent physical systems of ultra-cold gases (e.g. bosonic gases, fermionic gases, \nand spin mixtures). In particular, we consider the BCS-state as a rst trial example \nto show that there is a strong variation in the particle-number statistics at the \ncrossover from a superuid-BCS state to a Bose-Einstein condensate of molecules.
We propose a configuration of a magnetic microtrap that can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single-well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order to suppress these excitations, and conclude that such interferometer device should be feasible with currently available microtrap technique.
Precise alignment of an optical potential with a micrometer-scale magnetic trap near an atom chip is technically challenging compared with free-space systems. We investigate a double-well potential created by a focused, blue-detuned laser beam superimposed on an atom-chip magnetic trap for manipulating cold ⁸⁷Rb atoms. The measured separation of atomic clouds in the double well serves as a sensitive indicator of the laser focus: the separation reaches a minimum when the beam is aligned with the center of the magnetic trap. We develop a theoretical model for the combined magnetic and optical potentials and the resulting atomic motion, and validate its predictions using Monte Carlo simulations over a broad range of trap frequencies, barrier heights, and temperatures. Both the model and simulations show that optimal alignment corresponds to the minimum observable separation between the two atomic clouds. Parameter scans further reveal that stronger axial confinement and lower temperatures enhance the detectability of this minimum, providing a practical optical-alignment method for atom-chip systems in which direct beam characterization near the surface is difficult.
Cold atom interferometers have demonstrated excellent performance and hold great prospects for time, gravity, acceleration and rotation measurements [1]. Trapped interferometers, for example using atom chips [2], can potentially enable portable applications of theses sensors. Atom chip interferometers have been successfully demonstrated using Bose-Einstein condensates [3] but are subject to the effect of atom-atom interactions which cause phase decoherence [4]. In [5], we proposed an atom chip interferometer using a gas just above the condensation threshold to reduce the interaction effects. This proposal is similar to white light interferometry in the sense that the difference between the optical paths of the two arms must be close to zero to observe fringes. In a trapped interferometer this condition is analogous to maximizing the degree of symmetry between the two trapping potentials [6]. We demonstrated that if the two trapping potentials are harmonic with slightly different curvatures (ω and ω + δω for the first and the second trap) inhomogeneous dephasing arises.
We report on progress for a couple of experiments on manipulating cold atoms on a chip for quantum sensing. The first experiments are directed towards developing a compact atom interferometer on an atom chip using a double-well potential. The interferometer uses 87Rb atoms magnetically confined in an atomic waveguide produced by wires on the surface of a lithographically patterned chip. Finite element modeling of combinations of different current configurations with various external bias fields indicated a means of coherently splitting the atomic cloud through dynamically adjusting the currents and bias fields. In these experiments we investigate real-time transformations between different double-well configurations adiabatically and non-adiabatically, and study their effects on the initially trapped atoms. Coherence properties of the two atomic wavepackets are examined. In another set of experiments we investigate the properties of bosons confined to (quasi) one dimension in our magnetic waveguide. When the atom-atom repulsive interaction becomes much larger than the kinetic energy, bosons confined in one dimension can enter a new state of matter, the Tonks-Girardeau gas, in which they behave like non-interacting fermions. However, the bosons can still occupy the same momentum state and therefore the gas cannot be fully described by either Bose-Einstein or Fermi-Dirac statistics. This transition has been observed in optical lattices but not in magnetic atom chip waveguides. We discuss the conditions for obtaining a Tonks-Girardeau gas with 87Rb atoms in our atom chip waveguide as well as a novel signature for observing the transition in our system.
We report the coherent manipulation of internal states of neutral atoms in a magnetic microchip trap. Coherence lifetimes exceeding 1 s are observed with atoms at distances of 5-130 microm from the microchip surface. The coherence lifetime in the chip trap is independent of atom-surface distance within our measurement accuracy and agrees well with the results of similar measurements in macroscopic magnetic traps. Because of the absence of surface-induced decoherence, a miniaturized atomic clock with a relative stability in the 10(-13) range can be realized. For applications in quantum information processing, we propose to use microwave near fields in the proximity of chip wires to create potentials that depend on the internal state of the atoms.